Answer:
a)
Reduced Row Echelon:
![\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/6av3mrtqv9b83pjfaqme7dgcdynt93so71.png)
Solution to the system:

b)
Reduced Row Echelon:
![\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/oa1wdmcaxpv8wclzjr6l3yagrkoqre04zf.png)
Solution to the system:
x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.
Explanation:
To find the reduced row echelon form of the matrices, let's use the Gaussian-Jordan elimination process, which consists of taking the matrix and performing a series of row operations. For notation, R_i will be the transformed column, and r_i the unchanged one.
a)
![\left[\begin{array}{cccc}0&4&7&0\\2&1&0&0\\0&3&1&-4\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/td6poow3a9cp01f70qgsu58ccxl9sznpom.png)
Step by step operations:
1. Reorder the rows, interchange Row 1 with Row 2, then apply the next operations on the new rows:

Resulting matrix:
![\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&3&1&-4\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/dizx94g9jgn9hu963dssa5eq1fvpm2oxk0.png)
2. Set the first row to 1

Resulting matrix:
![\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/6av3mrtqv9b83pjfaqme7dgcdynt93so71.png)
3. Write the system of equations:

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

b)
![\left[\begin{array}{cccc}4&3&0&7\\8&6&2&-3\\4&3&2&-10\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/ld6swom972t8ou9el2lmbebr9vferr0d6r.png)
1.

Resulting matrix:
![\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]](https://img.qammunity.org/2020/formulas/mathematics/college/oa1wdmcaxpv8wclzjr6l3yagrkoqre04zf.png)
2. Write the system of equations:

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:
x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.